How can we master the mixed operation of rational numbers?

Mixed operations on rational numbers.

1) The key to performing mixed operations on rational numbers is to be proficient in the arithmetic, arithmetic, arithmetic and arithmetic rules and order of addition, subtraction, multiplication, division and multiplication. For more complex mixed operations, you can generally divide the equation into several segments according to the addition and subtraction operations in the question, and when calculating, start from the power of each segment and operate in order, with brackets to calculate the brackets first, and at the same time pay attention to the flexible use of the law of operation to simplify the operation.

2) When performing mixed operations on rational numbers, it should be noted that: first, we should pay attention to the order of operations, first calculate the operation of the higher level, and then calculate the operation of the lower level; The second is to pay attention to observation and flexibly use the arithmetic law to perform simple calculations to improve the speed and ability of arithmetic.

In fact, this is not difficult, the main thing is to be careful when calculating.

There are also symbolic transformations: () is preceded by "+", and the parentheses do not change, for example, 3+(5)=3+5, a+(-b)=a-b; "-:(", preceded by "-", must be changed in parentheses, for example, 3-(-5)=3+5, a-(b-c)=a-b+c

For absolute values, no matter what symbol is in front of them, the numbers in them must be positive after removing the absolute values. For example: 3-|-5|=3-5，3+|-5|=3+5。

The addition and subtraction symbols of rational numbers will be messed up, mainly parentheses and absolute values. If you understand the above, don't be careless by removing the brackets and absolute values in the formula when you do the question. Do more questions and master the proficiency and you should have no problem.

Seeing that your previous math foundation is not bad, I believe that after mastering it, there is an easier way to understand it yourself.

It's like this in science, sometimes a question will suddenly be blocked and you need to be enlightened. When you figure it out, it'll be fine.

The mixed operation of rational numbers is an arithmetic that contains a variety of operations such as addition, subtraction, multiplication, division, and multiplication.

1. Addition operation: the sum of two numbers that are opposite to each other gets 0; Two numbers that are opposite to each other can be added first; Numbers with the same denominator can be added first.

2. Subtraction operation: subtracting a number is equal to adding the opposite number of the number.

3. Multiplication operation: the same sign is positive, the different sign is negative, and the absolute value is multiplied; Multiply several numbers that are not equal to zero, first determine the sign of the product, and then multiply the absolute values.

4. Division: Divide by a number that is not equal to zero, which is equal to multiplying this number'Reciprocal; Zero cannot be a divisor and denominator; Division and multiplication of rational numbers are inverse operations.

Mixed operation of rational numbers refers to the simultaneous operation of different rational numbers in the calculation process, including addition, subtraction, multiplication and division.

1.Simplification first, then calculation

When performing a mixed operation of rational numbers, the equation should be simplified first, and the expression in parentheses should be calculated to be excited, and then the operation should be carried out. This avoids making mistakes and improves the accuracy of calculations.

2.Pay attention to the use of symbols

In the mixed operation of rational numbers, the use of different symbols and disadvantages, will have an impact on the results. For example, subtraction can be converted to addition, multiplication can be converted to division, and these conversion rules can be used to simplify calculations.

3.Calculation priority

In a mixed operation of rational numbers, the calculation should be performed according to the priority of the operation. The usual priority is multiplication and division followed by addition and subtraction, which means that multiplication and division are calculated first, and then addition and subtraction.

4.Deal with negative numbers

In the mixed operation of rational numbers, special attention should be paid to the treatment of negative numbers. The operation between negative numbers follows the principle that negative and negative are positive, which is consistent with the operation rules between positive numbers.

5.Use parentheses wisely

In mixed operations with rational numbers, the use of parentheses can change the priority of the operation, and the reasonable use of parentheses can make the calculation clearer. In mixed operations on rational numbers, when it comes to addition and subtraction, there may be situations where borrowing or carrying is required. Mastering the methods of borrowing and carrying can avoid calculation errors.

6.Pay attention to the conversion of decimal to fraction

In the operation of rational number mixture, it may involve the conversion between decimal and fraction. Mastering how to convert between decimals and fractions makes calculations easier. In the mixed operation of rational numbers, root number expressions may appear, and you can try to simplify the root number expressions and convert them into the form of rational numbers to facilitate calculation.

7.Double-count validation

When performing mixed operations on rational numbers, you can perform repeated calculation verification, that is, substitute the calculation results into the original equation for verification to ensure the accuracy of the calculation. When solving practical problems, it is necessary to flexibly use the skills of mixed operation of rational numbers, apply abstract mathematical concepts to practical situations, and help solve practical problems.

Rational numbers are a collective term for positive integers, 0s, negative integers, and fractions, and are a collection of integers and fractions. The mixed operation of rational numbers is a combination of the five operations of addition, subtraction, multiplication, division and power of rational numbers, so how to solve this combination, let's take a look.

The law of rational number arithmetic

1. The mixed operation of addition, subtraction, multiplication and division of rational numbers, if there is no parentheses to indicate what operation to do first, it shall be carried out in the order of multiplication and division first, then addition and subtraction, and if it is a homogeneous operation, it shall be calculated in order from left to right.

2. In the equation without parentheses, if there is only addition and subtraction or only multiplication and division, it should be calculated from left to right.

3. In the equation without parentheses, if there is both multiplication and division and addition and subtraction, the multiplication and division must be calculated first, and then the addition and subtraction.

4. In the formula with parentheses, it is necessary to calculate the ones in the parentheses first, and then the ones in the brackets.

The law of operation of rational numbers

The rational use of arithmetic laws is the basic guarantee for improving the ability to operate rational numbers, and when applying them, we must first understand the names of various arithmetic laws and the methods used.

1. The commutative law of addition and the law of association are usually used in addition and subtraction operations at the same time, the purpose of exchange is to combine, and the combination is generally based on positive and negative combinations, combined according to opposite numbers, in short, the numbers that are easy to calculate are combined.

2. The commutative law of multiplication and the associative law are usually used in multiplication and division operations, and the purpose of exchanging the early is also to combine, and the numbers that can be divided are generally combined when combined.

3. The distributive law is the distribution of multiplication to addition, which can be used either positively or reversely, but special attention should be paid to the fact that there is no distributive law between division and addition.

Addition and subtraction: first into the form of algebraic sum, then add and subtract, subtract a number is equal to add the opposite of this number, you can use the commutative law, the associative law.

Multiplication and division: Dividing by a number is equal to multiplying the reciprocal of this number, and commutative and associative laws can be used.

Addition, subtraction, multiplication and division: multiplication and division first, then addition and subtraction, with parentheses first calculated in parentheses, commutative property, associative law, and distribution rate can be used.

2.minus two-thirds [(minus two-thirds of the mammoth line) -2]=28 27

3.[(3) -50 )] Sharp key -2) =

Cubic - (branch - eighth) (4) = -5 2

I'm going to do this, I've just started junior high school, I hope I can help you!